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Probabilistic Methods · Bayesian Models and Methods

William Denault, Karl Tayeb, Peter Carbonetto, Jason Willwerscheid, Matthew Stephens

Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that can be leveraged to improve estimation of the underlying structure. However, existing methods that leverage side information are limited in the types of data they can incorporate, and they assume specific parametric models. Here, we introduce a novel method for this problem, *covariate-moderated empirical Bayes matrix factorization* (cEBMF). cEBMF is a modular framework that accepts any type of side information that is processable by a probabilistic model or a neural network. The cEBMF framework can accommodate different assumptions and constraints on the factors through the use of different priors, and it adapts these priors to the data. We demonstrate the benefits of cEBMF in simulations and in analyses of spatial transcriptomics and collaborative filtering data. A PyTorch-based implementation of cEBMF with flexible priors is available at https://github.com/william-denault/cebmf_torch.

General Machine Learning · Representation Learning

Berker Demirel, Marco Fumero, Francesco Locatello

Deep learning systems deployed in real-world applications often encounter data that is different from their in-distribution (ID). A reliable model should ideally abstain from making decisions in this out-of-distribution (OOD) setting. Existing state-of-the-art methods primarily focus on feature distances, such as k-th nearest neighbors and distances to decision boundaries, either overlooking or ineffectively using in-distribution statistics. In this work, we propose a novel angle-based metric for OOD detection that is computed relative to the in-distribution structure. We demonstrate that the angles between feature representations and decision boundaries, viewed from the mean of in-distribution features, serve as an effective discriminative factor between ID and OOD data. We evaluate our method on nine ImageNet-pretrained models. Our approach achieves the lowest FPR in 5 out of 9 ImageNet models, obtains the best average FPR overall, and consistently ranking among the top 3 across all evaluated models. Furthermore, we highlight the benefits of contrastive representations by showing strong performance with ResNet SCL and CLIP architectures. Finally, we demonstrate that the scale-invariant nature of our score enables an ensemble strategy via simple score summation.

General Machine Learning · Causality

Dominik Meier, Sujai Hiremath, PROMIT GHOSAL, Kyra Gan

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Probabilistic Methods · Bayesian Models and Methods

Russell Tsuchida, Jiawei Liu, Cheng Soon Ong, Dino Sejdinovic

Squared families of probability distributions have been studied and applied in numerous machine learning contexts. Typically, they appear as likelihoods, where their advantageous computational, geometric and statistical properties are exploited for fast estimation algorithms, representational properties and statistical guarantees. Here, we investigate the use of squared families as prior beliefs in Bayesian inference. We find that they can form helpful conjugate families, often allowing for closed-form and tractable Bayesian inference and marginal likelihoods. We apply such conjugate families to Bayesian regression in feature space using end-to-end learnable neural network features. Such a setting allows for a rich multi-modal alternative to Gaussian processes with neural network features, often called deep kernel learning. We demonstrate our method on few shot learning, outperforming existing neural methods based on Gaussian processes and normalising flows.

General Machine Learning · Representation Learning

Raphael Romero, Tijl De Bie, Nick Heard, Alexander Modell

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and the statistical stability of the extracted features. Despite this tradeoff, reminiscent of time–frequency tradeoffs in signal processing, most methods rely on a \emph{fixed temporal resolution}. Choosing an appropriate resolution parameter is typically difficult, and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales. We address this challenge by proposing ANIE ($\textbf{A}$daptive $\textbf{N}$etwork $\textbf{I}$ntensity $\textbf{E}$stimation), a multi-resolution framework designed to automatically identify the time scales at which network structure evolves, enabling the joint detection of both rapid and gradual changes. Modeling interactions as Poisson processes, our method proceeds in two steps: (1) estimating a low-dimensional subspace of node behavior, and (2) deriving a set of novel *empirical affinity coefficients* that measure change in interaction intensity between latent factors and support statistical testing for structural change across time scales. We provide theoretical guarantees for subspace estimation and the asymptotic behavior of the affinity coefficients, enabling model-based change detection. Experiments on synthetic networks show that ANIE adapts to the appropriate time resolution, and is able to capture sharp structural changes while remaining robust to noise. Furthermore, applications to real-world data showcase the practical benefits of ANIE’s multiresolution approach to detecting structural change over fixed resolution methods. An open-source implementation of the method is available at [https://github.com/aida-ugent/anie].

Social Aspects · Privacy-preserving Statistics and Machine Learning

Wenxuan Bao, Shan Jin, Hadi Abdullah, Anderson Nascimento, Vincent Bindschaedler, Yiwei Cai

Deep learning models are vulnerable to privacy attacks due to their tendency to memorize individual training examples. Theoretically-sound defenses such as differential privacy can defend against this threat, but model performance often suffers. Empirical defenses may thwart existing attacks while maintaining model performance but do not offer any robust theoretical guarantees. In this paper, we explore a new strategy based on the concept of plausible deniability. We introduce a training algorithm called **P**lausibly **D**eniable **S**tochastic **G**radient **D**escent (PD-SGD). The core of this approach is a rejection sampling technique, which probabilistically prevents updating model parameters whenever a mini-batch cannot be plausibly denied. We provide theoretical results showing that PD-SGD effectively mitigates privacy leakage from individual data points. Experiments demonstrate the scalability of PD-SGD and the favorable privacy-utility trade-off it offers compared to existing defense methods.

Probabilistic Methods · Bayesian Models and Methods

Amir Hossein Rahmati, Sanket Jantre, Weifeng Zhang, Yucheng Wang, Byung-Jun Yoon, Nathan Urban, Xiaoning Qian

Low-Rank Adaptation (LoRA) offers a cost-effective solution for fine-tuning large language models (LLMs), but it often produces overconfident predictions in data-scarce few-shot settings. To address this issue, several classical statistical learning approaches have been repurposed for scalable uncertainty-aware LoRA fine-tuning. However, these approaches neglect how input characteristics affect the predictive uncertainty estimates. To address this limitation, we propose Contextual Low-Rank Adaptation (**C-LoRA**) as a novel uncertainty-aware and parameter efficient fine-tuning approach, by developing new lightweight LoRA modules contextualized to each input data sample to dynamically adapt uncertainty estimates. Incorporating data-driven contexts into the parameter posteriors, C-LoRA mitigates overfitting, achieves well-calibrated uncertainties, and yields robust predictions. Extensive experiments on LLaMA2-7B models demonstrate that C-LoRA consistently outperforms the state-of-the-art uncertainty-aware LoRA methods in both uncertainty quantification and model generalization. Ablation studies further confirm the critical role of our contextual modules in capturing sample-specific uncertainties. C-LoRA sets a new standard for robust, uncertainty-aware LLM fine-tuning in few-shot regimes. Although our experiments are limited to 7B models, our method is architecture-agnostic and, in principle, applies beyond this scale; studying its scaling to larger models remains an open problem. Our code is available at https://github.com/ahra99/c_lora.

Computer Vision · Image and Video Generation

Wenjie Li, Xiangyi Wang, Heng Guo, Guangwei Gao, Zhanyu Ma

Old-photo face restoration poses significant challenges due to compounded degradations such as breakage, fading, and severe blur. Existing pre-trained diffusion-guided methods either rely on explicit degradation priors or global statistical guidance, which struggle with localized artifacts or face color. We propose Self-Supervised Selective-Guided Diffusion (SSDiff), which leverages pseudo-reference faces generated by a pre-trained diffusion model under weak guidance. These pseudo-labels exhibit structurally aligned contours and natural colors, enabling region-specific restoration via staged supervision: structural guidance applied throughout the denoising process and color refinement in later steps, aligned with the coarse-to-fine nature of diffusion. By incorporating face parsing maps and scratch masks, our method selectively restores breakage regions while avoiding identity mismatch. We further construct VintageFace, a 300-image benchmark of real old face photos with varying degradation levels. SSDiff outperforms existing GAN-based and diffusion-based methods in perceptual quality, fidelity, and regional controllability. Code link: https://github.com/PRIS-CV/SSDiff.

Fan Chen, Zeyu Jia, Alexander Rakhlin, Tengyang Xie

Reinforcement learning with outcome-based feedback faces a fundamental challenge: when rewards are only observed at trajectory endpoints, how do we assign credit to the right actions? This paper provides the first comprehensive analysis of this problem in online RL with general function approximation. We develop a provably sample-efficient algorithm achieving $\widetilde{O}({C_{\rm cov} H^3}/{\varepsilon^2})$ sample complexity, where $C_{\rm cov}$ is the coverability coefficient of the underlying MDP. By leveraging general function approximation, our approach works effectively in large or infinite state spaces where tabular methods fail, requiring only that value functions and reward functions can be represented by appropriate function classes. Our results also characterize when outcome-based feedback is statistically separated from per-step rewards, revealing an unavoidable exponential separation for certain MDPs. For deterministic MDPs, we show how to eliminate the completeness assumption, dramatically simplifying the algorithm. We further extend our approach to preference-based feedback settings, proving that equivalent statistical efficiency can be achieved even under more limited information. Together, these results constitute a theoretical foundation for understanding the statistical properties of outcome-based reinforcement learning.

General Machine Learning · Transfer, Multitask and Meta-learning

Hyeongyu Kim, GeonHui Han, Dosik Hwang

In recent advancements in Test Time Adaptation (TTA), most existing methodologies focus on updating normalization layers to adapt to the test domain. However, the reliance on normalization-based adaptation presents key challenges. First, normalization layers such as Batch Normalization (BN) are highly sensitive to small batch sizes, leading to unstable and inaccurate statistics. Moreover, normalization-based adaptation is inherently constrained by the structure of the pre-trained model, as it relies on training-time statistics that may not generalize well to unseen domains. These issues limit the effectiveness of normalization-based TTA approaches, especially under significant domain shift. In this paper, we introduce a novel paradigm based on the concept of a \textit{Buffer} layer, which addresses the fundamental limitations of normalization layer updates. Unlike existing methods that modify the core parameters of the model, our approach preserves the integrity of the pre-trained backbone, inherently mitigating the risk of catastrophic forgetting during online adaptation. Through comprehensive experimentation, we demonstrate that our approach not only outperforms traditional methods in mitigating domain shift and enhancing model robustness, but also exhibits strong resilience to forgetting. Furthermore, our \textit{Buffer} layer is modular and can be seamlessly integrated into nearly all existing TTA frameworks, resulting in consistent performance improvements across various architectures. These findings validate the effectiveness and versatility of the proposed solution in real-world domain adaptation scenarios. The code is available at https://github.com/hyeongyu-kim/Buffer_TTA.

Probabilistic Methods

Timo Löhr, Paul Hofman, Felix Mohr, Eyke Hüllermeier

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.

Probabilistic Methods

Brandon Feng, David Park, Xihaier Luo, Arantxa Urdangarin, Shinjae Yoo, Brian Reich

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Chenfei Gu, Qiangqiang Zhang, Ting Li, Jinhan Xie, Niansheng Tang

The growing prevalence of streaming data and increasing concerns over data privacy pose significant challenges for traditional nonparametric regression methods, which are often ill-suited for real-time, privacy-aware learning. In this paper, we tackle these issues by first proposing a novel one-pass online functional stochastic gradient descent algorithm that leverages the Huber loss (H-FSGD), to improve robustness against outliers and heavy-tailed errors in dynamic environments. To further accommodate privacy constraints, we introduce a locally differentially private extension, Private H-FSGD (PH-FSGD), designed to real-time, privacy-preserving estimation. Theoretically, we conduct a comprehensive non-asymptotic convergence analysis of the proposed estimators, establishing finite-sample guarantees and identifying optimal step size schedules that achieve optimal convergence rates. In particular, we provide practical insights into the impact of key hyperparameters, such as step size and privacy budget, on convergence behavior. Extensive experiments validate our theoretical findings, demonstrating that our methods achieve strong robustness and privacy protection without sacrificing efficiency.

Applications

Wei Sun, Wen Yang, Pu Jian, Qianlong Du, Fuwei Cui, Shuo Ren, Jiajun Zhang

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models (LLMs), even without supervised fine-tuning (SFT). However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions. To address this limitation, we propose Key-token Advantage Estimation (KTAE)—a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

General Machine Learning · Representation Learning

Zhijian Zhou, Liuhua Peng, Xunye Tian, Feng Liu

The relative similarity testing aims to determine which of the distributions, $P$ or $Q$, is closer to an anchor distribution $U$. Existing kernel-based approaches often test the relative similarity with a fixed kernel in a manually specified alternative hypothesis, e.g., $Q$ is closer to $U$ than $P$. Although kernel selection is known to be important to kernel-based testing methods, the manually specified hypothesis poses a significant challenge for kernel selection in relative similarity testing: Once the hypothesis is specified first, we can always find a kernel such that the hypothesis is rejected. This challenge makes relative similarity testing ill-defined when we want to select a good kernel after the hypothesis is specified. In this paper, we cope with this challenge via learning a proper hypothesis and a kernel simultaneously, instead of learning a kernel after manually specifying the hypothesis. We propose an anchor-based maximum discrepancy (AMD), which defines the relative similarity as the maximum discrepancy between the distances of $(U, P)$ and $(U, Q)$ in a space of deep kernels. Based on AMD, our testing incorporates two phases. In Phase I, we estimate the AMD over the deep kernel space and infer the potential hypothesis. In Phase II, we assess the statistical significance of the potential hypothesis, where we propose a unified testing framework to derive thresholds for tests over different possible hypotheses from Phase I. Lastly, we validate our method theoretically and demonstrate its effectiveness via extensive experiments on benchmark datasets. Codes are publicly available at: https://github.com/zhijianzhouml/AMD.

Social Aspects · Trustworthy Machine Learning

Mizuki Niihori, Shuichi Nishino, Teruyuki Katsuoka, Tomohiro Shiraishi, Kouichi Taji, Ichiro Takeuchi

In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep $k$-nearest neighbor (deep $k$NN) AD stands out for its interpretability and flexibility, leveraging distance-based scoring in deep latent spaces. Despite its strong performance, deep $k$NN lacks a mechanism to quantify uncertainty—an essential feature for critical applications such as industrial inspection. To address this limitation, we propose a statistical framework that quantifies the significance of detected anomalies in the form of $p$-values, thereby enabling control over false positive rates at a user-specified significance level (e.g.,0.05). A central challenge lies in managing selection bias, which we tackle using Selective Inference—a principled method for conducting inference conditioned on data-driven selections. We evaluate our method on diverse datasets and demonstrate that it provides reliable AD well-suited for industrial use cases.

General Machine Learning · Everything Else

Noa Shoham, Ron Dorfman, Shalev Shaer, Kfir Y. Levy, Yaniv Romano

Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator. In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models. To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.

Probabilistic Methods · Bayesian Models and Methods

Jean Feng, Avni Kothari, Lucas Zier, Chandan Singh, Yan Shuo Tan

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between exploring a sufficiently large set of concepts versus controlling the cost of obtaining concept extractions, resulting in a large interpretability-accuracy tradeoff. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. Even though LLMs can be miscalibrated and hallucinate, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. Across image, text, and tabular datasets, BC-LLM outperforms interpretable baselines and even black-box models in certain settings, converges more rapidly towards relevant concepts, and is more robust to out-of-distribution samples.

Computer Vision · Image and Video Generation

Jie Liu, Gongye Liu, Jiajun Liang, Yangguang Li, Jiaheng Liu, Xintao Wang, Pengfei Wan, Di ZHANG, Wanli Ouyang

We propose Flow-GRPO, the first method to integrate online policy gradient reinforcement learning (RL) into flow matching models. Our approach uses two key strategies: (1) an ODE-to-SDE conversion that transforms a deterministic Ordinary Differential Equation (ODE) into an equivalent Stochastic Differential Equation (SDE) that matches the original model's marginal distribution at all timesteps, enabling statistical sampling for RL exploration; and (2) a Denoising Reduction strategy that reduces training denoising steps while retaining the original number of inference steps, significantly improving sampling efficiency without sacrificing performance. Empirically, Flow-GRPO is effective across multiple text-to-image tasks. For compositional generation, RL-tuned SD3.5-M generates nearly perfect object counts, spatial relations, and fine-grained attributes, increasing GenEval accuracy from $63\%$ to $95\%$. In visual text rendering, accuracy improves from $59\%$ to $92\%$, greatly enhancing text generation. Flow-GRPO also achieves substantial gains in human preference alignment. Notably, very little reward hacking occurred, meaning rewards did not increase at the cost of appreciable image quality or diversity degradation.

Applications · Genetics, Cell Biology, etc

Payam Dibaeinia, Chris German, Suyash Shringarpure, Adam Auton, Aly A. Khan

Predicting disease risk from DNA presents an unprecedented emerging challenge as biobanks approach population scale sizes ($N>10^6$ individuals) with ultra-high-dimensional features ($L>10^5$ genotypes). Current methods, often linear and reliant on summary statistics, fail to capture complex genetic interactions and discard valuable individual-level information. We introduce **PRSformer**, a scalable deep learning architecture designed for end-to-end, multitask disease prediction directly from million-scale individual genotypes. PRSformer employs neighborhood attention, achieving linear $O(L)$ complexity per layer, making Transformers tractable for genome-scale inputs. Crucially, PRSformer utilizes a stacking of these efficient attention layers, progressively increasing the effective receptive field to model local dependencies (e.g., within linkage disequilibrium blocks) before integrating information across wider genomic regions. This design, tailored for genomics, allows PRSformer to learn complex, potentially non-linear and long-range interactions directly from raw genotypes. We demonstrate PRSformer's effectiveness using a unique large private cohort ($N \approx 5$M) for predicting 18 autoimmune and inflammatory conditions using $L \approx 140$k variants. PRSformer significantly outperforms highly optimized linear models trained on the *same individual-level data* and state-of-the-art summary-statistic-based methods (LDPred2) derived from the *same cohort*, quantifying the benefits of non-linear modeling and multitask learning at scale. Furthermore, experiments reveal that the advantage of non-linearity emerges primarily at large sample sizes ($N > 1$M), and that a multi-ancestry trained model improves generalization, establishing PRSformer as a new framework for deep learning in population-scale genomics.